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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.1.g.a 380.g 95.d $2$ $0.190$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}^{2}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{9}+q^{11}+\cdots\)
380.1.o.a 380.o 95.h $2$ $0.190$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}+q^{11}+\zeta_{6}^{2}q^{19}+\cdots\)
380.1.x.a 380.x 95.m $4$ $0.190$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(2\) \(0\) \(q+(-\zeta_{12}^{2}+\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots\)
380.2.a.a 380.a 1.a $1$ $3.034$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{9}-4q^{11}-4q^{13}+\cdots\)
380.2.a.b 380.a 1.a $1$ $3.034$ \(\Q\) None None \(0\) \(2\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+6q^{13}+\cdots\)
380.2.a.c 380.a 1.a $2$ $3.034$ \(\Q(\sqrt{2}) \) None None \(0\) \(-4\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{3}+q^{5}+(-2-2\beta )q^{7}+\cdots\)
380.2.a.d 380.a 1.a $2$ $3.034$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+2q^{7}+(1+2\beta )q^{9}+\cdots\)
380.2.c.a 380.c 5.b $4$ $3.034$ \(\Q(\sqrt{-2}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
380.2.c.b 380.c 5.b $6$ $3.034$ 6.0.14077504.2 None None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+\cdots\)
380.2.d.a 380.d 380.d $16$ $3.034$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}-\beta _{6}q^{5}+\cdots\)
380.2.d.b 380.d 380.d $40$ $3.034$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
380.2.f.a 380.f 76.d $20$ $3.034$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{12}q^{2}+\beta _{10}q^{3}+\beta _{16}q^{4}-q^{5}+\cdots\)
380.2.f.b 380.f 76.d $20$ $3.034$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{15}q^{2}+\beta _{9}q^{3}-\beta _{19}q^{4}+q^{5}+\cdots\)
380.2.i.a 380.i 19.c $2$ $3.034$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(1\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-4q^{7}+\cdots\)
380.2.i.b 380.i 19.c $6$ $3.034$ 6.0.1783323.2 None None \(0\) \(1\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}-\beta _{5})q^{3}+(1+\beta _{4})q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
380.2.i.c 380.i 19.c $8$ $3.034$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(-1\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{7}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
380.2.k.a 380.k 20.e $2$ $3.034$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\cdots\)
380.2.k.b 380.k 20.e $2$ $3.034$ \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
380.2.k.c 380.k 20.e $52$ $3.034$ None None \(-2\) \(-2\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
380.2.k.d 380.k 20.e $52$ $3.034$ None None \(2\) \(2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$
380.2.l.a 380.l 95.g $8$ $3.034$ 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-6\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{6}q^{5}+(-1+\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{7}+\cdots\)
380.2.l.b 380.l 95.g $12$ $3.034$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(\beta _{3}-\beta _{8})q^{5}+\beta _{6}q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)
380.2.n.a 380.n 76.f $40$ $3.034$ None None \(-3\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{6}]$
380.2.n.b 380.n 76.f $40$ $3.034$ None None \(3\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{6}]$
380.2.r.a 380.r 95.i $20$ $3.034$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{11})q^{3}+(-\beta _{7}+\beta _{13})q^{5}+\cdots\)
380.2.s.a 380.s 380.s $112$ $3.034$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
380.2.u.a 380.u 19.e $18$ $3.034$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{3}-\beta _{7})q^{3}-\beta _{4}q^{5}+(\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots\)
380.2.u.b 380.u 19.e $18$ $3.034$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{13}q^{3}+(\beta _{2}-\beta _{11})q^{5}+(-\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
380.2.v.a 380.v 380.v $4$ $3.034$ \(\Q(\zeta_{12})\) None None \(-4\) \(6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{12}^{3})q^{2}+(2-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
380.2.v.b 380.v 380.v $4$ $3.034$ \(\Q(\zeta_{12})\) None None \(2\) \(-6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+\zeta_{12}+\cdots)q^{3}+\cdots\)
380.2.v.c 380.v 380.v $216$ $3.034$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
380.2.y.a 380.y 95.l $4$ $3.034$ \(\Q(\zeta_{12})\) None None \(0\) \(6\) \(2\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+(1+\cdots)q^{5}+\cdots\)
380.2.y.b 380.y 95.l $36$ $3.034$ None None \(0\) \(-6\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{12}]$
380.2.bb.a 380.bb 380.ab $336$ $3.034$ None None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
380.2.bd.a 380.bd 95.p $60$ $3.034$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
380.2.be.a 380.be 76.k $120$ $3.034$ None None \(-3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
380.2.be.b 380.be 76.k $120$ $3.034$ None None \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
380.2.bh.a 380.bh 95.r $120$ $3.034$ None None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{36}]$
380.2.bj.a 380.bj 380.aj $672$ $3.034$ None None \(-12\) \(0\) \(-24\) \(0\) $\mathrm{SU}(2)[C_{36}]$
380.3.b.a 380.b 4.b $72$ $10.354$ None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
380.3.e.a 380.e 19.b $12$ $10.354$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(-1+\beta _{6}-\beta _{11})q^{7}+\cdots\)
380.3.g.a 380.g 95.d $4$ $10.354$ \(\Q(\sqrt{-6}, \sqrt{14})\) None None \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-5q^{5}+\beta _{2}q^{7}+5q^{9}+4q^{11}+\cdots\)
380.3.g.b 380.g 95.d $4$ $10.354$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(9\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(2-\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{7}-9q^{9}+\cdots\)
380.3.g.c 380.g 95.d $12$ $10.354$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(1+\beta _{3})q^{5}+\beta _{8}q^{7}+(6-\beta _{2}+\cdots)q^{9}+\cdots\)
380.3.h.a 380.h 20.d $108$ $10.354$ None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
380.3.j.a 380.j 380.j $232$ $10.354$ None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
380.3.m.a 380.m 5.c $36$ $10.354$ None None \(0\) \(-4\) \(10\) \(22\) $\mathrm{SU}(2)[C_{4}]$
380.3.o.a 380.o 95.h $40$ $10.354$ None None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{6}]$
380.3.p.a 380.p 380.p $232$ $10.354$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
380.3.q.a 380.q 76.g $160$ $10.354$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
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